Import Question JSON

Current Question (ID: 17540)

Question:

$\text{If the space between two convex lenses of glass in the combination shown in the figure below is filled with water, then:}$

Options:

1. $\text{the focal length of the system will decrease.}$
2. $\text{the focal length of the system will increase.}$
3. $\text{the power of the system will increase.}$
4. $\text{the power of the system will become infinite.}$

Solution:

$\text{Hint: Water between the lenses will behave as a concave lens.}$ $\text{Step 1: Draw a diagram showing the radius of curvature according to sign convention.}$ $R_1 = R$ $R_2 = -R$ $\text{Step 2: Find the power for the water lens}$ $\frac{1}{f_w} = \left(\mu_w - 1\right)\left[\frac{-1}{R} - \frac{1}{R}\right]$ $= (-ve)$ $\Rightarrow P \text{ is } (-ve)$ $\text{Step 3: Identify the change in power of the optical device}$ $P_{sys} = P_1 + P_2 + P_3$ $= P_1 + P_3 - (P_2)$ $\text{Here, } P_{sys} \downarrow$ $\text{And, } P_{sys} = \frac{1}{f_{sys}}$ $\text{Thus, the focal length of the system will increase.}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}